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March, 1974 Comparison of Linear Normal Experiments
Ole Havard Hansen, Erik N. Torgersen
Ann. Statist. 2(2): 367-373 (March, 1974). DOI: 10.1214/aos/1176342672

Abstract

Consider independent and normally distributed random variables $X_1,\cdots, X_n$ such that $0 < \operatorname{Var} X_i = \sigma^2; i = 1,\cdots, n$ and $E(X_1,\cdots, X_n)' = A'\beta$ where $A'$ is a known $n \times k$ matrix and $\beta = (\beta_1,\cdots, \beta_k)'$ is an unknown column matrix. (The prime denotes transposition.) The cases of known and totally unknown $\sigma^2$ are considered simultaneously. Denote the experiment obtained by observing $X_1,\cdots, X_n$ by $\mathscr{E}_A$. Let $A$ and $B$ be matrices of, respectively, dimensions $n_A \times k$ and $n_B \times k$. Then, if $\sigma^2$ is known, (if $\sigma^2$ is unknown) $\mathscr{E}_A$ is more informative than $\mathscr{E}_B$ if and only if $AA' - BB'$ is nonnegative definite (and $n_A \geqq n_B + \operatorname{rank} (AA' - BB'))$.

Citation

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Ole Havard Hansen. Erik N. Torgersen. "Comparison of Linear Normal Experiments." Ann. Statist. 2 (2) 367 - 373, March, 1974. https://doi.org/10.1214/aos/1176342672

Information

Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0289.62011
MathSciNet: MR370847
Digital Object Identifier: 10.1214/aos/1176342672

Subjects:
Primary: 62B15
Secondary: 62K99

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 2 • March, 1974
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